Hi LadyD
These little stems are called suckers and if you don't nip them out before they get any longer than 4-5 cm, they will grow into another stem on the tomato plant. So basically, if you want a strong single-stemmed plant that only needs simple staking instead of a tomato cage, nip out all the suckers. I am growing tomatoes in pots for the first time this year and because I didn't nip the suckers, my plants have gone pretty wild. As a result, I have had to battle the recent strong winds by driving in several stakes into each pot. It's not really very practical.
You can see my vegetable growing efforts at cluelessgardenerindubai.blogspot.com
Does anyone know what the thinking is behind nipping out all the little shoots that start to grow between the main stem and a side stem on tomato plants? I keep trying to remember to leave one plant one year un-nipped just to see the difference between the nipped and the non-nipped ... but catch myself finger-pinching everything out.